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Subtraction of Algebraic Expressions

If x - y = ...

Question

If $x - y = - 6$ and $x y = 4$ , find the value of $x^{3} - y^{3}$ .

- 288

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288

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- 28

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None of these

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Solution

The correct option is A $- 288$
$x - y = - 6, x y = 4$
$(x - y)^{3} = x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2} = - 216$
$= x^{3} - y^{3} - 3 y x (x - y) = - 216$
$x^{3} - y^{3} = - 216 + 3 (4) (- 6)$
$x^{3} - y^{3} = - 288$

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